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124 Decision making under uncertainty
exceed it by a significant amount of time, they are likely to gain a
substantial amount of goodwill from the customer and an enhanced
reputation throughout the industry. However, to increase the chances
of meeting the target, Decanal would have to hire extra labor and operate
some 24-hour working, which would increase their costs. Thus
the company has two conflicting objectives: (1) minimize the time
that the project overruns the target date and (2) minimize the cost
of the project.
For simplicity, we will assume that Decanal’s project manager has
two options: (1) work normally or (2) hire extra labor and work 24-hour
shifts. His estimates of the probabilities that the project will overrun the
target date by a certain number of weeks are shown on the decision
tree in Figure 5.16. The costs of the project for the two options and for
different project durations are also shown on the tree. (Note that, once
a given option is chosen, the longer the project takes to complete, the
greater will be the costs because labor, equipment, etc. will be employed
on the project for a longer period.)
To analyze this problem we need to derive a multi-attribute utility
function which will enable the project manager to compare the two
options. This process is simplified if certain assumptions can be made.
The most important of these is that of mutual utility independence.
Work normally
Hire extra labor, etc.
0.1
0.6
0.3
0.8
0.2
Overrun
time
0 weeks
3 weeks
6 weeks
Project
cost
$50000
$60000
$80000
0 weeks $120000
1 week $140000
Figure 5.16 – A decision tree for the project manager’s problem